Analysis of an $$M/\begin{pmatrix}G_1\\ G_2\end{pmatrix}/1$$ Queue with Bernoulli Vacation and Server Breakdown

Begum, Anjana; Choudhury, Gautam

doi:10.1007/s40819-022-01481-4

Int. J. Appl. Comput. Math

2022

DOI: 10.1007/s40819-022-01481-4

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Analysis of an $$M/\begin{pmatrix}G_1\\ G_2\end{pmatrix}/1$$ Queue with Bernoulli Vacation and Server Breakdown

Anjana Begum

Gautam Choudhury

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2024

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Cited by 4 publications

References 38 publications

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A Markovian Queueing Model for Telecommunications Support Center with Breakdowns and Vacation Periods

Chettouf,

Bouchentouf,

Boualem

2024

Oper. Res. Forum

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A Markovian Queueing Model for Telecommunications Support Center with Breakdowns and Vacation Periods

Chettouf,

Bouchentouf,

Boualem

2024

Oper. Res. Forum

View full text Add to dashboard Cite

Study of a two types of general heterogeneous service queueing system in a single server with optional repeated service and feedback queue

Mahanta,

Kumar,

Choudhury

2024

Hacettepe Journal of Mathematics and Statistics

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This paper addresses a model on a single server queue and two service representatives. After a customer is served, he/she has the three options: opting for receive the same service again (re-service), joining as a new customer for another regular service (feedback), or leaving the service system altogether. To ensure the queueing system is Markovian, we introduce an additional variable (supplementary variable) and using this approach, we derive the explicit distribution of queue size at random and departure epochs. Additionally, we determine the distribution of response time, inter-departure time, and busy period. By using the embedded Markov chain technique we have also derived the queue size distribution at departure epoch. We have also presented the cost analysis of the model with some numerical examples. The numerical illustration validates our findings and provides valuable insights into the queuing system.

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A literature review on retrial queueing system with Bernoulli vacation

Micheal Mathavavisakan,

Indhira

2024

YUGOSLAV J OPERATION

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The retrial phenomenon occurs inherently in a wide range of queueing systems. The majority of retrial queueing models do not account for vacation. However, in practice, retrial queueing systems undergo vacations for maintenance or other reasons. In this study, we provide an in-depth analysis of the many possible retrial queueing systems when Bernoulli vacations are in effect. Moreover, this study outlines the key principles and reviews the relevant literature. The framework of a retrial queue with Bernoulli vacation has numerous applications in computer networking systems, manufacturing and production mechanisms, inventory systems, including network service, mail service and file transfer service, etc. Several retrial queueing systems have been investigated, notably M/M/1, M/M/C, M/G/1, M[X]/G/1, and Geo/G/1. Many other important situations, such as server interruption, feedback, G-queue, impatient customers, priority customers, etc., have been explored in relation to retrial queues with Bernoulli vacation and the results of these investigations are also highlighted. The foremost objective of this study is to help researchers, administrators and technical workers who want to use queuing theory to simulate congestion and need to know where to find details on the right models. Finally, some open problems and potential future lines of survey are also covered.

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Analysis of an $$M/\begin{pmatrix}G_1\\ G_2\end{pmatrix}/1$$ Queue with Bernoulli Vacation and Server Breakdown

Cited by 4 publications

References 38 publications

A Markovian Queueing Model for Telecommunications Support Center with Breakdowns and Vacation Periods

A Markovian Queueing Model for Telecommunications Support Center with Breakdowns and Vacation Periods

Study of a two types of general heterogeneous service queueing system in a single server with optional repeated service and feedback queue

A literature review on retrial queueing system with Bernoulli vacation

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